Organisers: Alan Champneys (Bristol), John King (Nottingham), John Mackenzie (Strathclyde) and Christina Surulescu (TU Kaiserslautern)
Cell motility, morphogenesis, and pattern formation are essential features of cell dynamics. The involved biochemical processes and biomechanical properties range from the intracellular level over cell surface dynamics, cell-cell and cell-tissue interactions up to the scale of cell population behaviour influencing organ formation and functioning.
Mathematical models handling biological events taking place on one or several such scales can provide a powerful framework to understand these phenomena, test experimentally suggested conjectures, and make predictions about the behaviour of the studied system. Current modelling approaches are often continuous, involving systems of partial differential equations of various kinds (e.g., reaction-diffusion-transport, taxis, kinetic transport, population balance), possibly coupled to ordinary, random, or stochastic differential equations. Furthermore, the so-called agent-based approaches (e.g., cellular automata, Potts models, etc.) characterize the behaviour of individual cells or intracellular particles in a discrete way, permitting rather detailed descriptions of motions, interactions etc. Yet other model types are hybrids between discrete and continuous descriptions. Applications include, but are not restricted to embryogenesis, tumour growth and invasion, wound healing, tissue bioengineering, biofilms, etc. The models lead to highly complex analytical and numerical problems, which often call for the development of new mathematical tools or for the enhancement of existing ones. At the same time recent mathematical developments for example in nonlinear waves and coherent structures, in solid mechanics and in dynamical systems theory can help shed light on generic mechanisms; as well as the biology providing challenges to the mathematical state of the art.
Therefore, the aim of this workshop is to bring together scientists working on these timely and challenging topics of mathematical biology, analysis and numerics. It will provide both an international framework and motivation to further develop the modelling of the mentioned biological phenomena and to strengthen the synergies between the involved branches of applied mathematics, but also between mathematics and life sciences.